# $${\mathcal {PT}}$$PT-symmetric dimers with time-periodic gain/loss function

@article{Psiachos2014mathcalD,
title={\$\$\{\mathcal \{PT\}\}\$\$PT-symmetric dimers with time-periodic gain/loss function},
author={Demetra Psiachos and Nick Lazarides and Giorgos P. Tsironis},
journal={Applied Physics A},
year={2014},
volume={117},
pages={663-672}
}
• Published 2 June 2014
• Physics
• Applied Physics A
Abstract$${\mathcal {PT}}$$PT-symmetric dimers with a time-periodic gain/loss function in a balanced configuration where the amount of gain equals that of loss are investigated analytically and numerically. Two prototypical dimers in the linear regime are investigated: a system of coupled classical oscillators, and a Schrödinger dimer representing the coupling of field amplitudes, each system representing a wide class of physical models. Through a thorough analysis of their stability behavior…
7 Citations

## Figures from this paper

Dynamics of generalized PT-symmetric dimers with time-periodic gain–loss
• Mathematics, Physics
• 2014
A parity-time (PT)-symmetric system with periodically varying-in-time gain and loss modeled by two coupled Schrödinger equations (dimer) is studied. It is shown that the problem can be reduced to a
Photonic Floquet media with a complex time-periodic permittivity
• Physics
Physical Review B
• 2018
We study the exceptional point (EP) phenomena in a photonic medium with a complex time-periodic permiitivity, i.e., $\epsilon(t)=\epsilon_o+\epsilon_r*sin(\Omega t+\phi)$. We formulate the Maxwell's
Non-Convergent Perturbation Theory and Misleading Inferences about Parameter Relationships: the Case of Superexchange
We discuss the well-known three-center cation-anion-cation model for superexchange in insulating transition-metal compounds using limiting expansions for the Anderson-Hubbard model. We find that due
Exceptional Points of Degeneracy Induced by Linear Time-Periodic Variation
• Physics
Physical Review Applied
• 2019
We present a general theory of exceptional points of degeneracy (EPD) in periodically time-variant systems that do not necessarily require the presence of loss or gain and we show that even a single
Nonlinear waves in PT -symmetric systems
• Physics
• 2016
The concept of parity-time symmetric systems is rooted in non-Hermitian quantum mechanics where complex potentials obeying this symmetry could exhibit real spectra. The concept has applications in
Floquet protocols of adiabatic state flips and reallocation of exceptional points
• Physics
• 2018
We introduce the notion of adiabatic state flip of a Floquet Hamiltonian associated with a non-Hermitian system that it is subjected to two driving schemes with clear separation of time scales. The
Coherent perfect absorption in an electromagnetically induced transparency-like (EIT-like) system
• Physics
• 2016
We propose a scheme for realizing the coherent perfect absorption (CPA) by exploiting the moderate coupling between the electric and magnetic resonators in an electromagnetically induced

## References

SHOWING 1-10 OF 37 REFERENCES
$\mathcal{PT}$-symmetric nonlinear metamaterials and zero-dimensional systems
• Physics
• 2013
A one dimensional, parity-time ($\mathcal{PT}$)-symmetric magnetic metamaterial comprising split-ring resonators having both gain and loss is investigated. In the linear regime, the transition from
$\mathcal{PT}$-symmetric dimer of coupled nonlinear oscillators
• Physics
• 2013
We provide a systematic analysis of a prototypical nonlinea r oscillator system respecting PT -symmetry i.e., one of them has gain and the other an equal and opposite amount of loss. Starting from
Breathers in PT-symmetric optical couplers
• Physics
• 2012
We show that parity-time- ($\mathcal{PT}$-) symmetric coupled optical waveguides with gain and loss support localized oscillatory structures similar to the breathers of the classical
Asymmetric wave propagation through nonlinear PT-symmetric oligomers
• Physics
• 2012
In the present paper, we consider nonlinear PT-symmetric dimers and trimers (more generally, oligomers) embedded within a linear Schrodinger lattice. We examine the stationary states of such chains
Solitons in a chain of parity-time-invariant dimers.
• Physics, Medicine
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2011
A relation between stationary soliton solutions of the model and solitons of the discrete nonlinear Schrödinger (DNLS) equation is demonstrated, and approximate solutions forsolitons whose width is large in comparison to the lattice spacing are derived, using a continuum counterpart ofThe discrete equations.
Integrability of PT-symmetric dimers
• Physics
• 2013
The coupled discrete linear and Kerr nonlinear Schrodinger equations with gain and loss describing transport on dimers with parity-time (PT)-symmetric potentials are considered. The model is relevant
Discrete solitons in \chem {\cal PT} -symmetric lattices
• Physics, Mathematics
• 2012
We prove the existence of discrete solitons in infinite parity-time () symmetric lattices by means of analytical continuation from the anticontinuum limit. The energy balance between dissipation and
Gain-driven discrete breathers in PT-symmetric nonlinear metamaterials.
• Physics, Medicine
Physical review letters
• 2013
In the presence of nonlinearity, it is shown numerically that as a result of the gain and dissipation matching a novel type of long-lived stable discrete breathers can form below the lower branch of the band with no attenuation.
PT-symmetric oligomers: analytical solutions, linear stability, and nonlinear dynamics.
• Mathematics, Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2011
This work focuses on the case of (few-site) configurations respecting the parity-time (PT) symmetry, i.e., with a spatially odd gain-loss profile, with nontrivial properties in their linear stability and in their nonlinear dynamics.
Linear and nonlinear parity-time-symmetric oligomers: a dynamical systems analysis
• Physics, Medicine
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
• 2013
This work focuses on the cases of two- site (dimer) and three-site (trimer) configurations, i.e. oligomers, respecting the parity-time () symmetry, with different types of solutions of such configurations with linear and nonlinear gain/loss profiles.